\(S\)-convex, monotone, and positive interpolation with rational bicubic spline of \(C^ 2\)-continuity
type: Item
instance of: scholarly article
title: \(S\)-convex, monotone, and positive interpolation with rational bicubic spline of \(C^ 2\)-continuity
zbMATH Open document ID: 0791.65007
DOI: 10.1007/BF01990531
author: Jochen W. Schmidt
author: Walter Heß
published in: BIT
publication date: 1994-07-07T00:00:00Z
review text: The authors study certain bivariate rational cubic spline interpolants of the continuity class \(C^ 2\). Under certain conditions those splines are shape preserving, positive, monotone and preserve the so-called \(S\)- convexity of the data sets given on rectangular grids (the \(S\)-convexity implies the one-dimensional convexity in all directions with nonnegative ascent). To this end the authors propose and test a numerical search procedure.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 503587
zbMATH Keywords: monotone, and positive interpolation
zbMATH Keywords: \(C^ 2\)-continuity
zbMATH Keywords: \(S\)-convexity
zbMATH Keywords: bivariate rational cubic spline
zbMATH Keywords: shape preserving
zbMATH Keywords: monotone
MaRDI profile type: Publication
cites work: Monotonicity Preserving Surface Interpolation
cites work: Bicubic Spline Interpolation
cites work: Monotone Piecewise Bicubic Interpolation
cites work: An Algorithm for Monotone Piecewise Bicubic Interpolation
cites work: Q3827460
cites work: Q3488624
cites work: Shape-Preserving Bivariate Interpolation
cites work: Monotonicity preserving bicubic interpolation: A progress report
cites work: A survey on univariate data interpolation and approximation by splines of given shape
cites work: On superadditive rates of convergence
cites work: Rational biquadratic \(C^ 1\)-splines in \(S\)-convex interpolation
cites work: Q4000940
cites work: Positive, monotone, and \(S\)-convex \(C^ 1\)-interpolation on rectangular grids
cites work: Eingrenzung von Lösungen mit Hilfe der Regula falsi. (Inclusion of solutions by regula falsi)
cites work: Q3995192
Recommended article: Rational biquadratic \(C^ 1\)-splines in \(S\)-convex interpolation
Recommended article: Positivity and monotonicity preserving biquartic rational interpolation spline surface
Recommended article: Positivity preserving interpolation using rational bicubic spline
Recommended article: A criterion for the positivity of rational cubic \(C^ 2\)-spline interpolants
Recommended article: Q3364160
Recommended article: Positive quartic, monotone quintic \(C^ 2\)-spline interpolation in one and two dimensions
Recommended article: \(C^2\) positivity-preserving rational interpolation splines in one and two dimensions
Recommended article: Q4499543
Recommended article: Positive, monotone, and \(S\)-convex \(C^ 1\)-interpolation on rectangular grids
Recommended article: Q3132277
description: scientific article; zbMATH DE number 503587